The terms "a priori" and "a posteriori" are used in philosophy to distinguish between deductive and inductive reasoning, respectively. Attempts to define clearly or explain a priori and a posteriori knowledge are part of a central thread in epistemology, the study of knowledge. Since the definitions and usage of the terms have been corrupted over time and therefore vary between fields, it is difficult to provide universal definitions of them. One rough and oversimplified explanation is as follows: a priori knowledge is independent of experience, while a posteriori knowledge is dependent on experience. In other words, statements that are a priori true are tautologies.

Economists sometimes use "a priori" to describe a step in an argument the truth of which can be taken as self-evident. "A posteriori", on the other hand, implies that an argument must be based upon empirical evidence.

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History

Early uses

The phrases "a priori" and "a posteriori" are Latin for "from what comes before" and "from what comes later" (or, less literally, "[from first principles, but] before experience" and "after experience"). They appear in Latin translations of Euclid's Elements, a work widely considered during the early European modern period as the model for precise thinking.

An early philosophical use of what might be considered a notion of a priori knowledge (though not called by that name) is Plato's theory of recollection, related in the dialogue Meno (380 B.C.), according to which something like a priori knowledge is knowledge inherent, intrinsic in the human mind.

13th century philosopher Thomas Aquinas, in the Summa Theologica, writes: "Demonstration can be made in two ways: One is through the cause, and is called "a priori," and this is to argue from what is prior absolutely. The other is through the effect, and is called a demonstration "a posteriori"; this is to argue from what is prior relatively only to us. When an effect is better known to us than its cause, from the effect we proceed to the knowledge of the cause. And from every effect the existence of its proper cause can be demonstrated, so long as its effects are better known to us; because since every effect depends upon its cause, if the effect exists, the cause must pre-exist."

Immanuel Kant

The eighteenth-century German philosopher Immanuel Kant (1781) advocated a blend of rationalist and empiricist theories. Kant states, "although all our knowledge begins with experience, it does not follow that it arises from experience" According to Kant, a priori knowledge is transcendental, or based on the form of all possible experience, while a posteriori knowledge is empirical, based on the content of experience. Kant states, "... it is quite possible that our empirical knowledge is a compound of that which we receive through impressions, and that which the faculty of cognition supplies from itself (sensuous impressions giving merely the occasion)." Thus, unlike the empiricists, Kant thinks that a priori knowledge is independent of the content of experience; moreover, unlike the rationalists, Kant thinks that a priori knowledge, in its pure form, that is without the admixture of any empirical content, is knowledge limited to the deduction of the conditions of possible experience. These a priori, or transcendental conditions, are seated in one's cognitive faculties, and are not provided by experience in general or any experience in particular. Kant nominated and explored the possibility of a transcendental logic with which to consider the deduction of the a priori in its pure form. Concepts such as time and cause are counted among the list of pure a priori forms. Kant reasoned that the pure a priori forms are established via his transcendental aesthetic and transcendental logic. He claimed that the human subject would not have the kind of experience that it has were these a priori forms not in some way constitutive of him as a human subject. For instance, he would not experience the world as an orderly, rule-governed place unless time and cause were operative in his cognitive faculties. The claim is more formally known as Kant's transcendental deduction and it is the central argument of his major work, the Critique of Pure Reason. The transcendental deduction does not avoid the fact or objectivity of time and cause, but does, in its consideration of a possible logic of the a priori, attempt to make the case for the fact of subjectivity, what constitutes subjectivity and what relation it holds with objectivity and the empirical.

Johann Fichte

After Kant's death, a number of philosophers saw themselves as correcting and expanding his philosophy, leading to the various forms of German Idealism. One of these philosophers was Johann Fichte. His student (and critic), Arthur Schopenhauer, accused him of rejecting the distinction between a priori and a posteriori knowledge:

...Fichte who, because the thing-in-itself had just been discredited, at once prepared a system without any thing-in-itself. Consequently, he rejected the assumption of anything that was not through and through merely our representation, and therefore let the knowing subject be all in all or at any rate produce everything from its own resources. For this purpose, he at once did away with the essential and most meritorious part of the Kantian doctrine, the distinction between a priori and a posteriori and thus that between the phenomenon and the thing-in-itself. For he declared everything to be a priori, naturally without any evidence for such a monstrous assertion; instead of these, he gave sophisms and even crazy sham demonstrations whose absurdity was concealed under the mask of profundity and of the incomprehensibility ostensibly arising therefrom. Moreover, he appealed boldly and openly to intellectualintuition, that is, really to inspiration.|Schopenhauer|Parerga and Paralipomena, Vol. I, §13